Normal Force, Shear Force, Bending Moment and Torsion - Structural and Stress Analysis - page 55

X 1

W

X 2

S AB M BC

A B C

X 1

A X 2 C

M AB

W

S BC W

2

2

W W

2 x 2

x L x

L /2 L /2

(a) (b) (c)

W W

A B C

2 2

ve

B C

ve Bending

moment

A

WL /4

Change in S.F.
at B is W

ve

W W

2 2 (e)

(d)

A B C

F IGURE 3.13 Shear
force and bending
moment diagrams
for the beam of
Ex. 3.6

Deflected shape

(f)

beam, that

W
2 =

S AB + 0

which gives

W
2

S AB =−

S AB is therefore constant at all sections of the beam between A and B, in other words,
from a section immediately to the right of A to a section immediately to the left of B.

Now consider the free body diagram of the length X 2 C of the beam in Fig. 3.13(c).
Note that, equally, we could have considered the length ABX 2 , but this would have
been slightly more complicated in terms of the number of loads acting. For vertical
equilibrium of X 2 C

W
2 =

S BC − 0